Abstract

The importance of carbon in Earth's mantle greatly exceeds its modest abundance of ≈1,000–4,000 ppm. Carbon is a constituent of key terrestrial volatiles (CO, CO2, CH4), it forms diamonds, and it may also contribute to the bulk electrical properties of the silicate Earth. In contrast to that of the mantle, the carbon content of Earth's metallic core may be quite high (≈5 wt %), raising the possibility that the core has supplied carbon to the mantle over geologic time. The plausibility of this process depends in part upon the mobility of carbon atoms in the solid mantle. Grain boundaries of mantle minerals could represent fast pathways for transport as well as localized sites for enrichment and storage of carbon. Here, we report the results of an experimental study of grain-boundary diffusion of carbon through polycrystalline periclase (MgO) and olivine ([Mg,Fe]2SiO4) that were obtained by determining the extent of solid solution formation between a graphite source and a metal sink (Ni or Fe) separated by the polycrystalline materials. Experimental materials were annealed at 1,373–1,773 K and 1.5–2.5 GPa pressure. Calculated diffusivities, which range up to 10−11 m2·s−1, are fast enough to allow transport over geologically significant length scales (≈10 km) over the age of the Earth. Mobility and enrichment of carbon on grain boundaries may also explain the high electrical conductivity of upper mantle rocks, and could result in the formation of C-H-O volatiles through interactions of core-derived C with recycled H2O in subduction zones.

With the probable exception of the core, the silicate mantle is Earth's largest carbon reservoir, containing vastly more carbon than the atmosphere, oceans, and other near-surface reservoirs combined (1). However, the question of how carbon came to reside in the mantle, and where and in what form it is stored, remain largely unanswered. Carbon has a diminishingly small solubility in olivine and other major mantle minerals, implying that carbon must exist in separate C-rich phases such as carbonates, diamond, graphite, or C-H-O fluids (2). Carbon is also a candidate for one of the light-element “impurities” known to be present in the Fe-Ni core. It has been shown that Fe3C is stable at core temperatures and pressures (3–5), and these findings are complemented by the existence of graphite and carbides in iron meteorites (which represent planetary core fragments or unassembled core components). The presence of carbon in the core and/or lower mantle is also consistent with the hypothesis that a primitive C source exists deep in the Earth (6). To maintain a primitive C reservoir in the face of whole-mantle convection, this source would have to be largely isolated from convective flow (and sampled only accidentally by plumes) or replenished by continuous transfer from the core to the lower mantle. It has been suggested that such transfer might occur by diffusion or chemical reaction across the core–mantle boundary (CMB) (6). Regardless of its source and mobility, carbon is a critical element in determining the oxidation state of altervalent ions (e.g., of Fe, Cr, and V), the identity and abundance of C-H-O molecules, and the physical properties of the mantle. Carbon can affect redox conditions through chemical interactions with H and O, and if present along grain boundaries of mantle phases may lead to unexpectedly high electrical conductivity (7, 8).

In a previous study of carbon grain-boundary diffusion by Watson (9), it was concluded that carbon is immobile in grain boundaries of natural dunite, within the (limited) resolution of the beta-track mapping technique that was used (9). However, recent studies of grain-boundary diffusion in mantle minerals and analogs suggest that grain boundaries may represent sites for both rapid transport and chemical enrichment of elements that are incompatible in the lattice of these phases (10–12), and grain-boundary diffusion rates of other elements are high enough to imply diffusive transport distance as great as ≈100 km over the age of the Earth (10, 13). In light of these recent studies and because of the implications of carbon mobility in the mantle, we have revisited the issue of carbon grain-boundary diffusion.

In this study we examined grain-boundary diffusion of carbon in periclase (MgO) and magnesian olivine (Mg1.8Fe0.2SiO4). MgO is a stable, dense oxide that readily forms equilibrated microstructures and is present in the lower mantle as magnesiowüstite. Magnesian olivine is the dominant phase of the upper mantle at depths less than ≈400 km. Because the diffusant element of interest (C) is incompatible in lattices of these minerals, the general experimental strategy was to use a “source-sink” design that allows us to detect grain-boundary transport by measuring long-distance alloying of a carbon source with a metal sink separated from one another by polycrystalline oxide or silicate (Fig. 1). The efficacy of carbon grain-boundary transport was evaluated by measuring the C content of the metal wires or foils using an electron microprobe (EPMA). Complete experimental and analytical details can be found in Materials and Methods.

Setup for grain-boundary diffusion of carbon experiments. (a) Metal wire (Fe or Ni) was used as a carbon sink during radial diffusion; the graphite furnace is the carbon source. (b) Single/multiple layers of Ni foil were used as a carbon sink during planar diffusion; a high-purity graphite wafer is the carbon source. A silica glass sleeve was used to insulate the Ni sinks from “‘contamination” by the graphite furnace.

Results and Discussion

Our results indicate that carbon is indeed mobile in the grain boundaries of both periclase and olivine and resulted in 1–50 atom % alloying with the metal sink materials. In a given experiment, C concentrations varied by as much as a factor of 5 among analysis points in a single “detector” foil or wire. This observation is consistent with expected variability of grain-boundary “conductivities” with respect to carbon atoms: in a polycrystalline material with numerous grain boundaries of diverse lattice misorientation, the pathways encountered by diffusing C atoms are not expected to be equivalent in terms of either the solubility or the diffusivity of C. This variability notwithstanding, grain-boundary diffusion was an extremely effective transport pathway in experiments using both the radial and planar geometries. Average carbon concentrations for all experiments are reported in supporting information (SI) Table S1.

Results of radial grain-boundary diffusion experiments (MgO only) are shown in Fig. 2. The average C concentrations in Fe at 1,500° and 1,300°C are 12.5 and 5.4 atom %, respectively; consequently, there is an approximate 2-fold decrease in the C flux over this temperature range. Iron concentrations in the MgO indicate an oxygen fugacity (fO2) of ≈2 log units below the iron-wüstite (IW) oxygen buffer.† The average C concentrations in Ni at 1,500° and 1,300°C are 32.8 and 8.8 atom %, respectively; there is an approximate 2-fold decrease in the C flux over this temperature range. Carbon fluxes in the experiments with Ni wire are ≈3 times higher than those with Fe wire sinks. Nickel concentrations in the MgO indicate an fO2 of ≈3 log units below the nickel-nickel oxide (NiNiO) oxygen buffer.‡ Thus, the fO2 of the experiments run with Ni sinks is ≈3–4 log units higher than those run with Fe sinks. The results of these radial diffusion experiments suggest that fO2 may have a significant effect on the grain-boundary mobility of carbon in periclase.

Carbon fluxes in periclase (MgO) and olivine (Fo90). Fluxes calculated for experiments using linear diffusion geometry and Ni foil sinks as well as experiments using radial diffusion geometry and either a Ni or Fe wire sink.

Results of one-dimensional grain-boundary diffusion experiments featuring Ni foil(s) as carbon sinks are also shown in Fig. 2 for both the single-sink and multisink configurations. For periclase, the average C concentrations in Ni foil at 1,500° and 1,300°C are 18.5 and 8.4 atom %, respectively, in the single-sink experiments.§ Over a temperature range of 1,500°C to 1,100°C, average C concentrations range from 30.4 to 4.6 atom % in the first layer of the multisink experiments. Carbon concentrations and their corresponding fluxes in the first layer of the multisink experiments are consistently higher than in the single-sink experiments and also give results closer to those from the radial diffusion experiments. For olivine, the carbon flux at 1,500°C falls in the range of those calculated for periclase, but the flux at 1,300°C is significantly higher. The average C concentrations at 1,500° and 1,300°C in the first layer of Ni foil are 22.6 and 18.7 atom %, respectively.

In the multisink experiments, local partitioning equilibrium between the grain boundaries and the metal sink was assumed—that is, the C concentration in each Ni foil layer was taken to be proportional to the concentration of C in nearby grain boundaries. A plot of the C content of each foil vs. distance from the C source thus yields a concentration profile believed to reflect the average profile in the grain boundaries themselves. Fitting this surrogate profile to the standard constant-surface, error-function solution to the diffusion equation¶ yields an estimate of the grain-boundary diffusivity. The concentration “profiles” for the experiments involving periclase are shown in Fig. 3.‖ Estimated diffusivities range from 5.02E-11 m2/s at 1,500°C to 1.22E-11 m2/s at 1,100°C (Table S2). Although the number of data points is limited, the temperature dependence is systematic: a plot of ln D versus 1/T (Fig. 4) yields the Arrhenius relationship: D = 1.73E-8(±4.7E-9)exp(−70(±15)/RT), where Do is in m2/s, the activation energy EA is in kJ/mol, R is the absolute gas constant, and T is in K. Carbon concentration profiles obtained from experiments on olivine are relatively flat compared to those in periclase, and have nearly constant C content in the sinks that are farther from the carbon source (Fig. 5). The consistently high C content in all three foil horizons indicates very rapid diffusion, but also bring into question the appropriateness of the error function solution for extracting diffusivity. For this reason we resorted to use of the approximate diffusive length scale to estimate the diffusivity (D = x2/t, where D is diffusivity t is run duration, and x is the length of the diffusion profile). A linear fit to the data was used to extend the profile to the distance where C concentration goes to 0.48, which is taken as x. The diffusivities calculated in this way are 4.60E-11 m2/s at 1,500°C and 4.11E-11 m2/s at 1,300°C. At 1,300°C, diffusion in olivine is faster than in periclase, but the apparent lack of a temperature effect implies a much lower activation energy (≈14 kJ/mol), and thus diffusivities in olivine at higher temperatures may be significantly slower than those in periclase. However, given the less rigorous method in which these diffusivity values were obtained conclusions regarding the temperature dependence and activation energy of carbon diffusion in olivine should be considered preliminary. One possible explanation for the difference in activation energy between olivine and periclase could be the apparent effect of fO2. The radial diffusion experiments indicate that diffusivity increases with oxygen fugacity, which may imply that a fraction of the grain-boundary carbon exists as CO or CO2 molecules. At these experimental pressures, MgO may be reacting with CO2 and binding as a carbonate species, which then needs to be released to diffuse further. At higher pressures, olivine will also react with CO2, and thus activation energy for olivine at high pressures may be significantly higher than they are at 1.5 GPa.

Diffusion “profiles” in olivine (Fo90). These profiles are flat compared to the decreasing C content seen in the MgO profiles in Fig. 3, though C content is consistently high.

Fig. 6 shows the characteristic diffusion distance (
x=Dt) of carbon based on the calculated diffusivities in periclase over a period of 1 billion years. Using the Arrhenius relationship, carbon diffusivity was extrapolated down to core–mantle boundary temperatures (≈4,000°C on the mantle side). To estimate the compensating effect of increasing pressure with increasing temperature along the mantle geotherm (14), activation volumes of 1 cm3/mol and 3 cm3/mol were used to approximate diffusivity as a function of both P and T [for P = 1–15 GPa, T(K) = 1,900–1,420 (0.8P); for P = 16–140 GPa, T(K) = 1680 + 11.1 P] (Fig. S1). These curves represent characteristic transport distance based on diffusivities at fO2 conditions from the Ni experiments. Using the decreased fluxes of the Fe-wire experiments—in which the fO2 was significantly lower and perhaps more appropriate to the lower mantle—the transport distances are projected to be lower by a factor of ≈5 relative to those shown in the figure. At upper mantle P–T conditions, the characteristic diffusion distance of carbon in periclase grain boundaries (as an analog for mantle material) is on the order of ≈1+ km over Earth's history. Depending on the actual activation volume, transport distances in the lower mantle may be as low as ≈10 s of meters or as high as ≈10 km. Given the similar fluxes and estimated diffusivities of carbon in olivine grain boundaries, the characteristic diffusion distance through olivine would be on the same order at temperatures close to those of our experimental conditions (extrapolations to higher temperatures are risky with olivine because the temperature dependence is not well constrained). In general, then, grain-boundary diffusion of carbon is rapid enough to operate over geologically significant length scales, suggesting that diffusive exchange of carbon between the core and lower mantle is plausible. There are, of course, limitations to the conclusions regarding core–mantle interactions that can be made from this study alone. A very large extrapolation is required to move from experimental pressures and temperatures to those at the core–mantle boundary. Of course, olivine does not exist in the lower mantle (the significance of carbon mobility in olivine in the upper mantle is discussed below, however) and carbon mobility in perovskite may be quite different from in an upper mantle Mg-silicate mineral such as olivine. MgO does exist in the lower mantle as ferropericlase, but only at ≈20% or less by volume, and not necessarily in an interconnected network of grains.

Projected transport distances (kilometers) as a function of temperature and corresponding pressure (the mantle geotherm) over a 1 billion year (1 Gyr) period. Numbers in parentheses refer to the activation volume used (in cm3/mol) to estimate the effect of pressure on grain-boundary diffusivity. Transport distances may be as high as 10 km.

The potential existence of free, mobile carbon residing in the grain boundaries of mantle rocks has several interesting implications. The electrical conductivity of the lower crust and upper mantle is anomalously high in some areas. The presence of carbon (as graphite) has been proposed as a way of explaining the high-conductivity regions, existing either as graphite lenses (structural features) (15, 16) or on olivine grain boundaries (8). Graphite films have been documented on grain boundaries of igneous rocks (17), although the conditions under which such a film would have formed are unclear. The results of this study suggest that grain boundary enrichment and diffusion of carbon could contribute to the formation of a carbon film on mineral grain boundaries, which could be capable of producing the high conductivity observed in some areas of the mantle. For a grain boundary width of ≈1 nm (1 nm is ≈10 atoms wide), a continuous film of carbon would require a minimum concentration of 10 atomic %, or 100 C atoms per nm3. Because we have estimated both the fluxes (J) and the diffusivity (D) of carbon in these experiments, the concentration of carbon in the grain boundaries can also be estimated. Assuming an instantaneous steady-state condition, the measured flux can be approximated as J = −D/dc;dx, where dx is the known diffusion distance multiplied by a tortuosity factor of 1.7. The estimated carbon concentrations in periclase grain boundaries range from 19 to 39 atomic %, and from 27 to 48 atomic % in olivine. This rough calculation suggests that something approaching a continuous carbon film may be present in the grain boundaries of these minerals.

Another possible consequence of a flux of free carbon through the mantle is the production of volatiles, such as methane or other C-H-O species, through interaction of C with recycled (subducted) H2O. This would mean that the Earth's volatile budget is not controlled by subduction and volcanism alone, but that carbon indigenous to the deep Earth may also participate in the global carbon cycle, which could influence the way scientists evaluate and model this cycle.

Finally, grain-boundary diffusion could represent a fractionation process that may be responsible for some isotopically “light” diamonds. Large departures from the typical mantle δ13C of −5‰ in mantle-derived diamonds have been attributed to either high-temperature fractionation processes (18) or a biogenic carbon source (19, 20). Isotopes are now known to be fractionated in geological systems by diffusion processes: lighter isotopes diffuse slightly faster than their heavy counterparts. In molten silicates, for example, the ratio of the diffusivities of two isotopes is inversely proportionate to their mass ratio raised to an exponent of ≈0.05–0.2 (21–23). Because the relative mass difference between 12C and 13C is significant (as it is for light isotopes in general), grain-boundary diffusion could be an effective mechanism in producing isotopically light sources of carbon.

Here, we have shown that carbon is mobile in grain boundaries of both periclase and olivine over a range of fO2 conditions. The diffusivity of carbon in these minerals is high enough to suggest that grain-boundary diffusion could occur over a geologically significant length scale and therefore be an important process in terms of the distribution and transport of carbon in the mantle. A diffusive flux of free carbon through the mantle (or even from the core) is thus a possibility, the implications of which have bearing on the electrical conductivity of the mantle, the Earth's cycling of volatiles, and the fractionation of carbon isotopes. Understanding the geochemical behavior of carbon will ultimately provide us with a better understanding of processes that operate in the deep Earth.

In closing, it is important to emphasize that we are not advocating diffusion alone as an effective way of moving carbon from the core throughout the entire mantle. The highest diffusivity values to which our data can plausibly be extrapolated do indeed “predict” diffusive length scales on the order of the tens of kilometers in 1 Gyr (provided the activation volume is small), but such values could apply only near the core–mantle boundary. We envision diffusion at more realistic length scales (e.g., one to tens of kilometers) “feeding into” the general convective overturn or plume flow of the mantle. It is the combination of fast grain-boundary diffusion with mantle convection that may be effective in bringing core-derived carbon close enough to Earth's surface to interact with recycled H2O or be sampled by volcanic processes (Fig. 7).

Schematic of the potential contribution of grain-boundary diffusion to carbon transport and distribution in the mantle.

Materials and Methods

Traditional methods of characterizing grain-boundary diffusion depend on the compatibility of the element of interest in the crystal lattice. However, in cases where the diffusant (C) can be presumed to exist primarily in the grain boundaries, its mobility may be undetected by most bulk analysis methods. Therefore, the characterization of grain boundary transport of carbon requires a different experimental strategy, using “source” and “sink” layers of metal to detect movement through grain boundaries. The carbon atoms are partitioned into grain boundaries at the source and diffuse along the boundaries until they encounter a sink phase (either Ni or Fe metal) into which they dissolve. The time-integrated grain boundary flux (Jgb) can be determined by measuring the total number of carbon atoms (n) accumulated in the metal sink in a given time:
where Aint is the effective cross-sectional area of the grain boundaries that is intersected by the sink phase.

The experimental strategy implemented here was twofold. The first type of experiment used a standard graphite furnace as a carbon source. A 6-mm piece of Norton MgO was drilled out to a depth of ≈4 mm with a very fine drill bit. A segment of Ni (Alfa Aesar; 99.98%) or Fe (Alfa Aesar; 99.99%) wire was inserted into the well, and then any open space was packed with MgO powder (Fig. 1a). This was placed in a standard 12.7-mm-diameter piston-cylinder assembly along with filler pieces of MgO and crushable alumina, held at 1,300–1,500°C and 2.5 GPa for 10 h, and then quenched. This method used radial inward diffusion of carbon from the graphite furnace “source” to the wire “sink.” Data extraction using this diffusion geometry is somewhat more complicated, because Aint decreases radially inward (it is not constant). The radial grain boundary cross-sectional area for these experiments was modeled to approximate the flux of carbon atoms. The average grain size was ≈75 μm, so the MgO matrix was divided into concentric shells, each a grain size in width; therefore, for an average radius of 1.5 mm, there were 20 shells. For a given angle θ and a wire length of ≈3 mm, the cross-sectional area of each shell can be calculated and plotted. Because the resulting profile is linear, the median value was taken, and then doubled, because the “slice” of wire analyzed by microprobe was experiencing a flux of atoms from either side, or from twice number of grain boundaries. Given the good agreement between the flux values calculated in this way and those calculated from the more direct planar experiments, it seems that this method yields a good approximation of the radial flux of carbon.

The second approach was to establish a one-dimensional gradient across a volume of MgO. Our technique involved prefabrication of MgO (periclase) and Fo90 (olivine) wafers (≈3 mm diameter × 1.5 mm thick). The sample was stacked as such: stock MgO wafer, Ni (Alfa Aesar 99.5%) foil, prefabricated periclase or olivine wafer, high-purity graphite wafer, stock MgO. These pieces was placed inside a silica glass sleeve, and the entire assemblage was placed in a modified 19-mm-diameter piston-cylinder assembly along with filler pieces of MgO and crushable alumina (Fig. 1b), held at 1,100–1,500°C and 1.5 GPa for 5 h, and then quenched. In some cases, multiple Ni foil sinks were used in series, with ≈1.5-mm periclase/olivine wafers in between. Implementation of Eq. 1 is more direct with this diffusion geometry and is described below.

Run products were mounted in epoxy and polished for analysis by electron microprobe (EPMA). Carbon coating, which is a routine procedure for EPMA, was not an option in this case because we would be measuring carbon in the metal. Instead, a conductive silver (Ag) paint was used to ground the wire/foil to the metal sample holder. This method was sufficient in preventing electrons from building up on the sample surface (“charging”). The samples were analyzed with a 15-kV accelerating potential and a 50-nA current with a beam size of 20 μm. For Fe and Ni, Kα x-rays were collected on a LIF crystal with a counting time of 10 s, using pure Fe and Ni metal standards, respectively; for C, Kα x-rays were collected on a PC2 crystal with a counting time of 60 s using a pure C standard. These analytical conditions resulted in a detection limit of ≈500 ppm C, which was well below the level required. To approximate the fO2 of the system, the concentration of Ni or Fe in the surrounding MgO was measured. This required the removal of the Ag paint followed by carbon coating, after C analyses have been made. In these analyses, Mg Kα x-rays were measured on a TAP crystal with a counting time of 10 s; analyses of Ni and Fe are as described above only with count times increased to 60 s, resulting in detection limits of ≈300 ppm for both Ni and Fe.

The raw microprobe data were used in conjunction with SigmaScan image software to determine the grain boundary volume in the sample and ultimately the flux of source atoms through the mineral grain boundaries. This was done by first calibrating the scale of the back scattered electron image, then using the software to determine the area of the Ni or Fe wire or foils. The two-dimensional image was assigned a depth of 10 μm, which seemed reasonable given the average grain size. This volume was then converted to a mass of Ni or Fe via its density, and thus the concentration of carbon in the sink, measured in atomic %, can be converted to the number of atoms and ultimately the mass of carbon. To determine the grain boundary volume, the total length of the grain boundaries was carefully measured, again with the software, and assigned a width of 1 nm. The distance between the source and sink horizons was measured and then multiplied by a factor of 1.7 to represent the tortuosity of the pathway. These three parameters—mass transport, grain boundary volume, and diffusion distance—plus the duration of the experiment, were then used to calculate the flux of the source element through the grain boundaries. This amounts to a practical implementation of Eq. 1 for a complex, polycrystalline sample.

Acknowledgments

We appreciate the insightful and helpful comments of the two reviewers. This work was supported by National Science Foundation Grant EAR-0337481 (to E.B.W.).

↵§ The measured C concentrations may exceed the known solubilities at 1 atm, and the high-pressure solubilities are unknown. The effect of limited C solubility in the metals may mean that the estimated fluxes are a lower bound.

↵¶ Determined by using the constant surface solution to Fick's second equation: , where C(x, t) is the carbon concentration in the foil, Co is the source concentration of carbon, x is the distance from the source, t is the run duration, and D is the diffusivity.

↵‖ The C concentration at the source should be the solubility of C in Ni at run conditions, rather than in graphite (100%). This would increase the calculated diffusivities; therefore, the values presented in this article represent a lower bound.

Physical and social well-being in old age are linked to self-assessments of life worth, and a spectrum of behavioral, economic, health, and social variables may influence whether aging individuals believe they are leading meaningful lives.